CHAPTER 4 FRAME SYNCHRONIZATION BY CYCLIC PREFIX
4.2 M ODIFIED ML A LGORITHM
4.3.4 VDSL Test Loops with Complex Topologies
The above procedure can be applied to other test loops with complex topologies as listed in the VLSI draft standard [35]. The estimated frame boundary θ and the averaged Et/N0 of all used tones for 8 kHz DMT VDSL downstream are listed in Table 1 and Fig. 4.8.
The first row in Table 1 contains the results from the conventional ML algorithm while the lower ones are from the modified ML algorithm.
Table 4.1 (θ , Et/N0) of VDSL test loops.
Loop No. VDSL1 VDSL2 VDSL3 VDSL4 VDSL5, 6, & 7 (43,-12) (42, -5) (43,-4.5) (43, -5) (42, -4) Short
(300 m) (37,35) (39,36) (37, 36) (40,30) (38,32) (59, 2) (58, 8) (58,-0.5) (58,26) (58, 2) Medium
(1000 m) (50,41) (48,32) (49,35) (55,38) (49,38) (70,17) (69, 3) (69, -4) (70,19) (70,10) Long
(1500 m) (61,24) (60,23) (60,20) (64,21) (61,33)
0 5 10 15
30 40 50 60 70
Fram e B oundary E s tim ated V alue
Delay
M ax im um Lik elihood M odified M L
0 5 10 15
-20 0 20 40 60
A veraged S NR
Tes t Loops
Et/No
Figure 4.8 θ and Et/N0 of VDSL test loops.
The order of test loops is arranged from short to long, with the index numbers from 1 to 15, respectively. In other words, VDSL1 to VDSL4 of 300 m long are indexed from 1 to
4, VDSL5 is 5, while VDSL1 to VDSL4 of 1000 m long are 6 to 9, VDSL6 is 10, etc. Since the topologies of these test loops contain various types of wires and some of them have bridged-taps, the performance differences of these two algorithms do not have smooth transition as the previous test cases. However, the bit-loading of each tone for short loop is high, and therefore the performance of the modified ML algorithm is much better than the conventional one, especially for short test loop.
4.4 Summary
In this chapter, a low-complexity modified ML algorithm for frame boundary estimation is developed. Its performance is better than the conventional one over the dispersive channel. A test environment is built to analyze the performance of DMT-based VDSL system. The analysis in this dissertation takes the AWGN noise into consideration and the transmission power is –60 dBm/Hz in the amateur radio bands. Simulation results show that the modified ML algorithm has better performance so that the Et/N0 of each tone is raised, especially for those carrying data of high-level QAM. The modified algorithm improves the VDSL system performance significantly because most of its sub-channels are loaded with a large number of bits.
Chapter 5 ISI Cancellation Algorithm for DMT-based VDSL System
For the traditional DMT-based VDSL system, there are still two drawbacks remained:
un-cancelled residual ISI outside the cyclic prefix and deterioration of channel capacity by TEQ. In this chapter3[43], we propose a algorithm to enhance the performance of the DMT- based VDSL system by minimizing the ISI effect.
Several techniques have been proposed to reduce or even remove the cyclic prefix in the OFDM system [43][44][45][46]. In [44], the residual ISI cancellation (RISIC) technique was first introduced to mitigate the residual ISI in an OFDM system with channel response longer than the guard interval. The corresponding receiver structure is shown in Fig. 5.1. Recently, there are some further studies to the RISIC algorithms. In [45], the author proposed a modified algorithm, denoted as Kim’s approach in this dissertation, with multiple processing iterations and the performance is better than the RISIC algorithm especially over the channel with a deep spectral null. However, it can be applied only in a low-level QAM system, such as 16-QAM constellations. Another method proposed in [46]
3 Part of the content in this chapter will be published in:
S. T. Lin and C. H. Wei, “Iterative ISI Cancellation for DMT-based VDSL Systems,” to appear in International Journal of Electrical Engineering. 中國電機工程學刊
improves the performance of RISIC algorithm by adding soft in and soft out (SISO) decision feedback to the whole system. It does improve the whole system performance slightly, with a tremendous increase in system complexity. In this chapter, we first apply the RISIC algorithm to the DMT-based VDSL system with reduced guard interval and compare its performance with traditional cyclic prefix system. Then we propose an iterative ISI cancellation with zero-padded (IIC-ZP) algorithm, a modification of RISIC algorithm with reasonable complexity, for DMT-based VDSL system to improve its performance, especially for the system without guard interval. There is another approach [47][48] using perfect equalization for DMT system without guard interval, however, it process the data in frequency domain instead of time domain.
5.1 System Model
In this section, a typical DMT-based VDSL system is introduced first, then the procedures of RISIC algorithm and Kim’s approach are derived. Finally, the proposed algorithm of IIC-ZP algorithm is discussed.
5.1.1 DMT-based VDSL System
The i-th transmitted DMT symbol in frequency domain can be expressed as Xi k, . The corresponding IFFT xi n, is the time domain signal after DMT modulation:
1 2 /
, ,
0
1 N j kn N
i n i k
k
x X e
N
− π
=
=
∑
, 0 n N 1≤ ≤ − ………..….(5.1)Cyclic prefix is added to xi n, before transmission:
{ }
, , , , , 1, ,0, , , 1
i n i N L i N i i N
s = x − L x − x L x − , 0≤ ≤ + −n N L 1
h
………(5.2)
Let the VDSL channel response of length M+1 be
{
h h0, ,1 hM}
=
h L ……….(5.3)
If the channel length is shorter than the cyclic prefix, i.e., M≤L, the received signal r can be represented as:
, ,(( ))
0 N
M
i n m i n m
m
r h x −
=
=
∑
, 0≤ ≤ −n N 1………(5.4)where ( )⋅ N denotes modulo by N.
Signal ri n, is a circular convolution of and h xi n, , only when M≤L. Otherwise, the residual ISI outside the cyclic prefix will degrade the system performance.
5.1.2 RISIC Algorithm
The RISIC algorithm [44], was originally proposed for the fixed and low bit-loading wireless OFDM application. The algorithm containing two major steps, tail cancellation and cyclic reconstruction, can be described as follows.
Step (1) : Previous symbol ISI tail cancellation:
0
, , 1
I
i n i n i n
r% =r −ζ −, , 0 n N≤ ≤ − ……….(5.5) 1
where is the previous symbol ISI tail after I-th iteration, as defined in Step (6), equation (5.9)
1, I i n
ζ −
Step (2) : Current symbol estimation:
0 0
, ,
ˆi k { }/i n k
X =FFT r% H ..………..(5.6)
where Hk is k-th channel response in frequency domain.
Step (3) : Cyclic reconstruction tail calculation:
Perform IFFT to current symbol ˆ0, to get , then calculate its tail portion
Step (4) : Current symbol cyclic reconstruction:
0 1
Step (6) : ISI tail calculation:
, 1,(( )) The above RISIC algorithm can be employed to the OFDM system with insufficient cyclic prefix length, even there is no guard interval between two symbols [44]. For DMT-based VDSL system, each sub-channel contains high-level QAM, the performance of RISIC algorithm is shown to be better than the traditional DMT system after one iteration
except when the system has no guard interval.
Restoration FFT 1-tap FEQ
Figure 5.1 Receiver block for iterative ISI cancellation.
5.1.3 Kim’s Approach
In this section, the Kim’s approach [45], which is improved from the RISIC algorithm, is described. Fig. 5.2 shows the block diagram of the proposed approach which proceeds as:
Step (1) : Optimal delay is estimated:
{ } ( ) Step (2) : Cyclic prefix portion of the current block is recovered:
{ }
Step (3) : Previous symbol ISI cancellation and cyclic prefix reconstruction are performed simultaneously:
where * stands for linear convolution.
Step (4) : , , are then converted to the frequency domain, and the frequency domain equalization is done and decisions are made to obtain
,
r%i n 0 n N≤ ≤ −
ˆ,
Xi k.
Although one block delay is introduced in Step (2), no intermediate decisions are used in this scheme.
Figure 5.2 Block diagram of the Kim’s approach.
5.1.4 IIC-ZP Algorithm
The IIC-ZP algorithm is derived from RISIC algorithm to improve the system performance, especially in the system without guard interval.
Modification 1: Select a peak delay ∆ for initial symbol estimation in Step (2) of RISIC algorithm. This concept is similar to reference [45], but the peak is defined in [49] as the highest energy of the channel response, which can be located by maximum likelihood (ML) algorithm for frame synchronization.
If the peak of the twisted-pair channel response is located at D delays from the beginning of the response, the selected data used for the zero-th iteration in equation (5.5) of current symbol estimation in the FFT operation is replaced by:
0 ,
r% , i n D≤ ≤ + −n N D 1.………(5.14) Selecting the peak delay at the initial estimation will improve the performance of the RISIC algorithm when there is no guard interval, as shown in Fig. 5.9. If the length of guard interval exists, this peak delay technique cannot be applied to the cyclic prefix system but it can be applied to the zero-padded system [50] instead.
Modification 2: Padding zeroes in guard interval between two symbols instead of cyclic prefix is used for reducing complexity in tail calculation process.
{ }
The received signal r is expressed as:, 1, 1,(( )
Then the previous symbol’s ISI tail in the Step (1) of RISIC is:
1, 1,(( ))
And Step (4) of RISIC, current symbol cyclic reconstruction, should be modified:
0
One advantage of the IIC-ZP algorithm is that ISI tail and cyclic reconstruction tail are identical, as shown in equations (5.16) to (5.18).
5.2 Computer Simulations
In this section, an example to illustrate the impact of the residual ISI on a DMT-based system is discussed first. Then the simulation results of the RISIC algorithm, Kim’s approach, and our proposed IIC-ZP algorithm are illustrated to observe their performances.
5.2.1 Influence of the Residual ISI for a DMT-based System
To see the influence caused by the ISI, an example is illustrated to demonstrate the relationship between the original information signals Xi k, , its corresponding IFFT signalxi n, , and the transmission signal with cyclic prefix si,n. The sizes of both FFT and IFFT are set to N=128 and the cyclic prefix length L=8 in this proposed example. The original signals Xi k, is set zero except the 4th and the 124th components to be 1+i and 1-i.
The corresponding IFFT signalxi n, will form as three sine waves in one period N=128, as shown in Fig. 5.3 with small dots. The transmission signal with cyclic prefix si,n, with circle point in Fig. 5.3, are formed by adding last 8 component in front ofxi n, . The received data, , is the results of convolution of transmission signal with the channel response H=[0.03
i n,
r
0.06 0.7 0.1 0.01 0.09 0.01], i.e.,M ≤L (L=8), is plotted in Fig. 5.4. The signals plotted by the‘*’ points are the convolution results of xi n, and H, while the circle points are the convolution results of si,n and H. From the simulation results, the received data is distorted by the channel effect, however, if the cyclic prefix is added, the perfect reconstructed is possible by using the N points of information from the received (N+L) points.
0 20 40 60 80 100 120 140
-0.02 -0.01 0 0.01 0.02 0.03
Magnitude
Time (t)
Original Data X i,n W ith Cyclic Prefix S
i,n
Figure 5.3 DMT signal in time domain with one active tone.
0 20 40 60 80 100 120 140 -0.02
-0.01 0 0.01 0.02 0.03
Magnitude
Time (t)
Xi,n*H Si,n*H
Figure 5.4 Received signal with channel length shorter than that of cyclic prefix.
However, if the channel length is longer than that of the cyclic prefix, the received data may be distorted seriously such that the perfect reconstruction is not possible no matter cyclic prefix is added or not, as shown in Fig. 5.5. In this example, the channel response H=[0.09 0.01 0.2 0.05 0.25 0.15 0.05 0.02 0.08 0.03 0.01 0.03 0.02 0.01], whose length is greater than L. Both the received data are distorted no matter the cyclic prefix is added or not.
0 20 40 60 80 100 120 140 -0.02
-0.01 0 0.01 0.02 0.03
Magnitude
Time (t)
Xi,n*H Si,n*H
Figure 5.5 Received signal with channel length longer than that of cyclic prefix.
5.2.2 Kim’s Approach and RISIC Performance in DMT-based VDSL
System
In this sub-section, the Kim’s approach is applied to the DMT-based DSL system to observe that if it can be applied to this system. At first, a normal bit-loading number calculated according to the SNR parameter of each sub-channel are applied to the system, however, the symbol error rate performance of this system is not acceptable. By reducing the maximum allowed bit number in each sub-channel, the performance could be improved as shown in Fig. 5.6. Since the Kim’s approach was proposed for the OFDM system with low-level QAM at each sub-channel, it is not suitable for our proposed DMT-based VDSL system with high-level QAM.
3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8
10-4 10-3 10-2 10-1 100
Sy mERbooarrr tel
Maximum Bit loading 100m
500m 1000m 1500m
Figure 5.6 Bit loading vs. symbol error rate for Kim’s approach.
Then, the RISIC algorithm is applied to the DMT-based VDSL system to see its performance. At first, if there is no cyclic prefix adding to the system, its performance is similar to the Kim’s approach. However, since this algorithm can be applied to the system with different lengths of the cyclic prefix and its number of iterations can also be adjusted.
Actually, the BER performance of the RISIC algorithm without iteration will be closed to that of traditional DMT-based system. For comparison, the simulation-results of the RISIC algorithms of the zeroth iteration are compared with the traditional DMT-based system, as shown in Fig. 5.7.
0 5 10 15 20 25 30 35
10-5 10-4 10-3 10-2 10-1 100
Guard Interval Length BE
R
RISIC DMT
Figure 5.7 Performance comparison of RISIC (iteration 0) and traditional DMT technology.
However, the BER performance of the RISIC algorithm can be improved by increasing the iteration number except that if the guard interval length is zero, as shown in Fig. 5.8. On the other hand, if there is no cyclic prefix, the BER performance is greater than
one tenth no matter how many iterations are calculated, as shown in Fig. 5.8. Therefore, a new approach, IIC-ZP algorithm is proposed in this dissertation to improve the BER performance of the system without cyclic prefix. And its performance is discussed in the following sub-section.
0 5 10 15 20 25 30 35
10-7 10-6 10-5 10-4 10-3 10-2 10-1 100
Guard Interval Length BE
R
RISIC(0) RISIC(1) RISIC(2)
Figure 5.8 Performance comparison of RISIC algorithm with different iterations.
5.2.3 Performance Comparison of IIC-ZP and RISIC Algorithms
To evaluate the performances of the proposed IIC-ZP scheme, a 200-m gauge #26 test loop with –140 dBm/Hz AWGN have been simulated and compared to the traditional DMT and RISIC scheme. All the following simulations are based on the assumption that channel response at the receiver side is known. A 1024-QAM (10 bits) is used in each sub-channel.
In simulations, the shorten impulse response type of TEQ [3] is used in the traditional DMT
system, and the energy ratio of the channel response power in the guard interval is 44 dB higher than outside the guard interval. While in RISIC and IIC-ZP system, the TEQ function is turned off during in this simulation. We simulated the systems with various guard interval lengths, from 0 to 32, and compare their BERs, as shown in Fig. 9. The performance of the IIC-ZP algorithm with two iterations, shown as IIC-ZP(2) in Fig. 9, is better than the traditional DMT system, which is plotted in dashed line. The value inside the parentheses means the number of iterations. For RISIC algorithm, the performances are plotted in dotted line for comparison. The performance of the IIC-ZP algorithm is close to that of the RISIC when the guard interval is greater than one but its performance is much better at zero guard interval case. If the recursive number is three, the guard interval length, L, can be reduced from 32 to 0 and the throughput can be increased to 6% (L/N+L, where N=512 and L=32).
The RISIC algorithm and IIC-ZP algorithm are able to process the received signals if the channel delay span is less than half of the symbol duration, and therefore the TEQ function block can be eliminated at the receiver block. To see the deterioration of channel capacity by TEQ, the performances of IIC-ZP after the second iteration with/ or without TEQ are illustrated in Fig. 5.10, and the performance of conventional DMT is also plotted for comparison. From the simulation results, we can see that the system without TEQ module has better performance. This is because the TEQ module is used to shorten the channel, but it also changes channel characteristics at the same time, and that may degrade the system performance.
From the above simulations, both the RISIC and our proposed IIC-ZP algorithms can be applied to a DMT VDSL system to improve the performance without decreasing the channel capacity by adding TEQ module and extend the usable bandwidth by reducing the length of guard interval. In addition, for the system without guard interval, our proposed IIC-ZP algorithm performs much better than the RISIC algorithm.
In summary, the RISIC algorithm and its modification IIC-ZP algorithm are applied to the high bit-loading DMT VDSL system. Their performances are compared with the traditional DMT system. These algorithms provide a more complete ISI cancellation scheme because they try to cancel all the ISI, including those outside the guard interval, i.e., residual ISI. Both the system performance and throughput can be improved at a reasonable cost of complexity increase.
0 5 10 15 20 25 30 35
10-7 10-6 10-5 10-4 10-3 10-2 10-1 100
Guard Interval Length BE
R
DMT RISIC(2) IIC-ZP(2) RISIC(3) IIC-ZP(3)
Figure 5.9 Performance comparison of DMT, RISIC and IIC-ZP receiver.
0 5 10 15 20 25 30 35 10-5
10-4 10-3 10-2 10-1
Guard Interval length BE
R
DMT-200m IIC-ZP-TEQ IIC-ZP-NO-TEQ
Figure 5.10 Performance comparison of IIC-ZP receiver with or without TEQ.
5.2.4 Residual ISI and Symbol Error Rate
From the previous derivations and simulations, it is clear that the ISI can degrade the BER performance of the DMT-based VDSL system. In this section, the effects of the ISI to the BER performance are discussed. First, a channel model is formulated with long tail of channel impulse response with length M such that it can create different level of residual ISI. For example, both a sine and reciprocal functions are selected to create the channel modeling as in equation (5.19). The corresponding waveform of this channel response is plotted in Fig. 5.11 with channel length equals to 80, i.e., M=80.
( ) ( ( ) )
( ) ( ( ) )
0 1
H n 0.1 sin 2.5 2 2 7 5
H n 0.64 0.8 / 5 8 5
n
n M n M
n M M n M
π
⎧ =
=⎪⎪⎨ ⋅ ⋅ ⋅ − ≤ ≤ +
⎪ = ⋅ − + ≤
⎪⎩ ≤ ………(5.19)
0 10 20 30 40 50 60 70 80
0 0.002 0.004 0.006 0.008 0.01 0.012
n Magnudeit
Figure 5.11 Channel response for residual ISI influence study.
The residual ISI is caused by the tail of channel response outside the guard-interval. To study the relationship of the residual ISI and the BER performance, the tail inside the guard interval energy ratio to the total channel is calculated first, as shown in Fig. 5.12. For clearly observation, the illustration is divided into four sections. The x-axis ‘n’ is the length of the guard interval while the y-axis is the ratio.
0 5 10 15 20 100
n rati
o
20 25 30 35 40
10-3 10-2 10-1 100
n
40 45 50 55 60
10-4 10-3 10-2
n
60 65 70 75 80
10-5 10-4 10-3
n
Figure 5.12 Energy ratio over various cyclic prefix lengths.
At first, the IIC algorithm is applied on the DMT-based system to show the BER performance with various guard interval length from 1 to M as well as different iteration times.
Fig. 5.13 shows part of the simulation results of the first iteration IIC algorithm with guard interval length from 48 to 76. In Fig. 5.14, the corresponding energy ratio outside the guard interval is plotted for reference. It can be seen from the simulation that if the energy ratio outside the guard interval is less than 8.0x10-4, the BER is greater than 10-1. Then the BER is improved from 10-1 to 10-7 as the energy ratio is changed from 2.1x10-3 to about 5.5x10-5.
45 50 55 60 65 70 75 80 10-7
10-6 10-5 10-4 10-3 10-2 10-1 100
n
BER
Figure 5.13 BER performance of the first iteration IIC algorithm.
45 50 55 60 65 70 75 80
10-5 10-4 10-3 10-2
n
Residual ISI energy ratio
Figure 5.14 Corresponding residual ISI energy ratio.
Similarly, Fig. 5.15 shows part of the simulation results of the second iteration IIC algorithm with guard interval length from 27 to 36. In fig 5.16, the corresponding energy ratio inside the guard interval is plotted for reference. The BER is improved from 2x10-3 to10-6 as the residual energy ratio is changed from 3.7x10-2 to about 8x10-3.
27 28 29 30 31 32 33 34 35 36
10-6 10-5 10-4 10-3 10-2 10-1 100
Guard Interval Length
BER
IIC(1) IIC(2)
Figure 5.15 BER performance of the IIC algorithm with one and two iterations.
27 28 29 30 31 32 33 34 35 36 10-3
10-2 10-1
n
Residual ISI energy ratio
Figure 5.16 Corresponding residual ISI energy ratio.
5.3 Summary
In this chapter, the RISIC algorithm and its modification, IIC-ZP algorithm, are applied to the high bit-loading DMT VDSL system. Their performances are compared with the traditional DMT system. These algorithms provide a more complete ISI cancellation scheme than that only using cyclic prefix approach. Both the system performance and throughput can be improved at a reasonable cost of complexity increase. Also, the relationship between the residual ISI and the BER performance are studied by simulations.
Chapter 6
Conclusions and Future Works
In this dissertation, basing on the architecture of traditional DMT-based ADSL system, the DMT-based VDSL system is proposed. To upgrade the ADSL system to achieve the
In this dissertation, basing on the architecture of traditional DMT-based ADSL system, the DMT-based VDSL system is proposed. To upgrade the ADSL system to achieve the